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Stability.

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Presentation on theme: "Stability."— Presentation transcript:

1 Stability

2 The stability of a cone.

3 Stability in the s-plane.

4 Tacoma Narrows Bridge (a) as oscillation begins
and (b) at catastrophic failure.

5 Tacoma Narrows Bridge (a) as oscillation begins
and (b) at catastrophic failure.

6

7 The Routh-Hurwitz Stability Criterion

8

9

10 Case 1: No element in the first column is zero.

11 Example 5.1 Second-order system

12 Example 5.2 Thrid-order system

13

14 Case 2: Zero in the first column

15

16 ExampIe 5.3 Unstable system

17 Case 3: Zeros in one row

18

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20 Example 5.4 Robot control

21

22 Welding head position control.

23

24

25 Relative Stability of Feedback Control Systems

26 Root locations in the s-plane.

27

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29 (a) Turning control system for a two-track vehicle.
(b) Block diagram.

30

31

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33 The stable region.

34 Closed-loop control system with T(s) = Y(s)/R(s) = 1/(s3 + s2+ 2s+24).

35 Routh array for the closed-loop control system
with T(s) = Y(s)/R(s) = 1/(s3 s2 2s 24)

36 The closed-loop disk drive head system with an optional velocity feedback.

37 Equivalent system with the velocity feedback switch closed.

38

39 Response of the system with velocity feedback. (a) MATLAB script.
(b) Response with Ka = 100 and K1 = 0.05.


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